Talk with Arianni in the Elven Alienage first. Then go and speak with Thrask in The Gallows, ask about Vincento to find out that he's going to be arrested, this is mainly necessary if Thrask doesn't tell you where Samson is. You can use that to speak to Vincento in Lowtown, if you tell him about the arrest he'll tell you where Samson is. Get the information from Samson, he'll tell you to go to the Docks.

When you visit the Docks at night, fight the enemies and head to Arthuris's Private Dock using your minimap. Be sure to loot the Abomination's body, you'll find a letter that will unlock the An Errant Letter quest. Next you'll head to Darktown. Be sure to pick up Sister Plinth's Remains near Danzig, this will unlock the quest The Remains of Sister Plinth.

Next you'll head to the Wounded Coast. Follow your minimap to enter the Slaver Caverns. You'll be attacked as soon as you get there. Keep following your minimap until you find the group of slavers with Feynriel. You've got a few ways of dealing with them:

Have Varric talk to Varian, he'll give you Feynriel and his purse and back down. Downside is you'll lose out on battle XP.

You can try to bribe the slavers.

Fight the slavers straight out.

If you're a rogue, pick the option where you kill Varian, you'll still have to fight the rest of the slavers, but it will be an easier fight.

Once you've freed him, you'll have to decide what to do with him. You'll score points with Aveline and Fenris if you send him to the Circle, but lose them with Anders, Merrill and Bethany. If you let him go to Dalish, you'll get points with Merrill and Anders, but lose points with Carver, Fenris and Aveline. If you send him to the Circle, you'll also be able to get the Elves at Large quest from the Chanter's Board in Act 2. Completing this quest either way will unlock the Act of Mercy quest. This quest is also one of the four that will unlock the Nice Crime You Have Around Here quest.